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Asymptotic Methods in Stochastics
Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.
Asymptotic Methods in Probability and Statistics
Hardbound. One of the aims of the conference on which this book is based, was to provide a platform for the exchange of recent findings and new ideas inspired by the so-called Hungarian construction and other approximate methodologies. This volume of 55 papers is dedicated to Miklos Csorgő a co-founder of the Hungarian construction school by the invited speakers and contributors to ICAMPS'97.This excellent treatize reflects the many developments in this field, while pointing to new directions to be explored. An unequalled contribution to research in probability and statistics.
Strong Approximations in Probability and Statistics
Strong Approximations in Probability and Statistics presents strong invariance type results for partial sums and empirical processes of independent and identically distributed random variables (IIDRV). This seven-chapter text emphasizes the applicability of strong approximation methodology to a variety of problems of probability and statistics. Chapter 1 evaluates the theorems for Wiener and Gaussian processes that can be extended to partial sums and empirical processes of IIDRV through strong approximation methods, while Chapter 2 addresses the problem of best possible strong approximations of partial sums of IIDRV by a Wiener process. Chapters 3 and 4 contain theorems concerning the one-ti...
Limit Theorems in Change-Point Analysis
Change-point problems arise in a variety of experimental and mathematical sciences, as well as in engineering and health sciences. This rigorously researched text provides a comprehensive review of recent probabilistic methods for detecting various types of possible changes in the distribution of chronologically ordered observations. Further developing the already well-established theory of weighted approximations and weak convergence, the authors provide a thorough survey of parametric and non-parametric methods, regression and time series models together with sequential methods. All but the most basic models are carefully developed with detailed proofs, and illustrated by using a number of data sets. Contains a thorough survey of: The Likelihood Approach Non-Parametric Methods Linear Models Dependent Observations This book is undoubtedly of interest to all probabilists and statisticians, experimental and health scientists, engineers, and essential for those working on quality control and surveillance problems. Foreword by David Kendall
Quantile Processes with Statistical Applications
Provides a comprehensive theory of the approximations of quantile processes in light of recent advances, as well as some of their statistical applications.
An Asymptotic Theory for Empirical Reliability and Concentration Processes
Mik16s Cs6rgO and David M. Mason initiated their collaboration on the topics of this book while attending the CBMS-NSF Regional Confer ence at Texas A & M University in 1981. Independently of them, Sandor Cs6rgO and Lajos Horv~th have begun their work on this subject at Szeged University. The idea of writing a monograph together was born when the four of us met in the Conference on Limit Theorems in Probability and Statistics, Veszpr~m 1982. This collaboration resulted in No. 2 of Technical Report Series of the Laboratory for Research in Statistics and Probability of Carleton University and University of Ottawa, 1983. Afterwards David M. Mason has decided to withdraw from this project. The authors wish to thank him for his contributions. In particular, he has called our attention to the reverse martingale property of the empirical process together with the associated Birnbaum-Marshall inequality (cf.,the proofs of Lemmas 2.4 and 3.2) and to the Hardy inequality (cf. the proof of part (iv) of Theorem 4.1). These and several other related remarks helped us push down the 2 moment condition to EX
